s2w4 Precalc FC Laws of sine and cosine

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one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

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Is the following an identity?

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Lets review congruent vs similar triangles - what is the difference?

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Lets review congruent triangles: you know two triangles are congruent if

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The angles of a triangle add up to

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ok, up until know, trig has been all about the right triangles. But we are about to push a little beyond that. This is called the law of sines

for ANY triangle, where A is the side opposite angle a, B is the side opposite angle b, and C is the side opposite angle C. Given this triangle with sides a, b and c, drag A B and C to their proper angles.

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

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setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

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At what angle would the radius of circle B only touch that initial line once?

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There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

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Given the following information about a triangle, which law can you use to find all the other sides?

Side, angle, side
Angle, side, angle
angle, angle, side
side, side, angle
side, side, side
angle, angle, angle

Law of sines
Law of cosines
this does not describe just one triangle

Trim End | 02:58

Questions 23 & 22 | 02:15

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Questions 23 & 22

02:15

Trim End | 02:31

Question 24 | 01:34

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Question 24

01:34

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Solve the triangle using Law of Sines.

a=_______ , b=_______ , C=_______ °
you will want to solve for angle C first, and round the lengths to the hundreth place. note that C should be in degrees.

1

solve the triangle using law of cosines
a = 6, b=10, c=11
A=_______ °, B=_______ °, C=_______ °
round to the nearest hundreth, 

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draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

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watching the proofs helps me understand the laws

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categorize

what the law of sines is
what the law of cosines is
when to use the law of sines
when to use the law of cosines
how to simplify or rearrange trig expressions using the identities I know
when are triangles congruent
why SSA gives an ambiguous case
how to use the law of sin to find the area of triangle

ive got this
im fuzzy
so confused

s2w4 Precalc FC Laws of sine and cosine

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

I don't remember the intersecting chord theorem. Do you?

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.